Methods and systems for determining a range rate for a backscatter transponder

ABSTRACT

Methods for determining a range rate of a backscatter transponder and readers implementing the methods are described. The reader transmits a continuous wave signal and receives a modulated reflected response signal from the transponder, mixes the modulated reflected response signal with the carrier frequency to produce a downconverted signal, bandpass filters the downconverted signal to pass a bandpass filtered signal containing at least the modulation frequency, applies a non-linear amplitude transfer function to produce a modulation-suppressed signal, and measures the frequency of the modulation-suppressed signal and determines the range rate from the measured frequency.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application claims priority to Canadian Patent Application No.2,824,704 filed on Aug. 26, 2013, the entirety of which is incorporatedby reference herein.

FIELD OF THE INVENTION

The present application relates to radio frequency identificationdevices (RFID), and in particular to determining the range rate of anRFID device relative to a reader based on backscatter modulated responsesignals.

BACKGROUND OF THE INVENTION

Intelligent transportation systems, such as ETC systems, use radiofrequency (RF) communications between roadside readers and transponderswithin or attached to vehicles. The readers form part of an automaticvehicle identification system for uniquely identifying vehicles in anarea, such as a toll plaza. Each reader emits a coded identificationsignal, and when a transponder enters into communication range anddetects the reader, the transponder sends a response signal. Theresponse signal contains transponder identification information,including a unique transponder ID. In the United States, currentITS-based, and in particular ETC-based, RF communication systems arelicensed under the category of Location and Monitoring Systems (LMS)through the provisions of the Code of Federal Regulations (CFR) Title 47Part 90 Subpart M.

Vehicle-mounted transponders may either be active or passive. Activetransponders contain a battery that powers the transponder. Eachtransponder listens for a trigger pulse or signal from a roadside readerand, upon sensing one, generates and transmits a response signal.Passive transponders rely upon energy supplied by the roadside reader inthe form of a continuous wave RF signal. The continuous wave signalenergizes the transponder and the transponder transmits its responsesignal by way of backscatter modulation of the continuous wave signal.Passive transponders may or may not include a battery in someimplementations.

In some situations, the road stations are designed to be “open road”,also known as “multi-lane free-flow”, meaning that communications areconducted at highway speed and there are no physical lane separations sovehicles are not constrained. In ETC systems this occurs with no gates,which means that transactions occur quickly, and also means that thereis no gate or barrier that prevents a vehicle without a validtransponder from traversing the toll plaza area. Open road ETC systemsrely upon ex post facto enforcement. For example, in manyimplementations an image is captured of each vehicle's license platearea. The image capture depends on a vehicle detection mechanism, suchas a light curtain or magnetic loop for detecting vehicle presence inthe roadway. The vehicle detection and image capture point is oftenoutside of the RF capture zone within which the vehicle-mountedtransponder communicates with the ETC system. The ETC system may betasked with correlating captured license plate images with processedtransponder-based toll transactions to determine whether any of thevehicle license plate images belong to a vehicle that did not complete asuccessful electronic toll transaction. That vehicle's owner may then besent an invoice for the toll amount.

In other ITS stations, the station may be measuring vehiclecharacteristics such as weight, or volume, or speed, and the system istasked with correlating the instrument measurements with processedtransponder-based transactions to associate the measurements to thevehicles. Image capture may also be used in such stations.

The challenge in any open road system is to quickly and accuratelycorrelate vehicle information from sensors, like license plate images,with the transponder communication transaction. In ETC systems it isparticularly important that the detected vehicles are correlated withprocessed toll transactions in order to identify which vehicle, if any,did not pay a toll via a transponder. One of the challenges in all thesesystems is to accurately estimate the path travelled by a vehicleassociated with a transponder that has completed a transaction, so thatthe vehicle's position can be correlated to the other sensors, e.g. avehicle identified by the vehicle detection system used by the imagecapture system.

BRIEF DESCRIPTION OF THE DRAWINGS

Reference will now be made, by way of example, to the accompanyingdrawings which show embodiments of the present invention, and in which:

FIG. 1 shows, in block diagram form, an example electronic tollcollection (ETC) system;

FIG. 2 shows, in block diagram form, a simplified block diagram of anRFID reader for determining Doppler shift in a backscatter RFID;

FIG. 3 shows, in block diagram form, a side-view of an example ETCsystem capture zone;

FIG. 4 shows a simplified block diagram of a planar view of vehiclespaths through an example ETC system capture zone;

FIG. 5 shows a simplified diagram of a range of position determinationsfor a vehicle in an ETC system capture zone;

FIG. 6 shows another simplified diagram of a range of positiondeterminations for a vehicle in an ETC system capture zone;

FIG. 7 shows a graph of example range rate magnitude measurements and acurve fit to the data;

FIG. 8 shows another graph of example range rate measurements with acurve fit to the data; and

FIG. 9 shows a further simplified diagram of a range of positiondeterminations for a vehicle in a multi-antenna ETC system capture zone.

Similar reference numerals are used in different figures to denotesimilar components.

DESCRIPTION OF SPECIFIC EMBODIMENTS

In one aspect, the present application describes a method of determininga range rate of a vehicle-mounted backscatter transponder in a roadwayusing an automatic vehicle identification system, the system includingan antenna defining a coverage area for communicating with thebackscatter transponder, the range rate being a rate of change of adistance between the transponder and the antenna. The method includestransmitting, via the antenna, a continuous wave signal having a carrierfrequency; receiving a modulated reflected response signal from thetransponder, wherein the modulation is at a modulation frequency;converting the modulated reflected response signal to a downconvertedsignal by mixing the modulated reflected response signal with thecarrier frequency; bandpass filtering the downconverted signal to pass abandpass filtered signal containing at least the modulation frequency;applying a non-linear amplitude transfer function to the bandpassfiltered signal to remove modulation and produce a modulation-suppressedsignal; measuring the frequency of the modulation-suppressed signal; anddetermining the range rate based upon a Doppler shift corresponding tothe measured frequency of the modulation-suppressed signal.

In another aspect, the present application describes a reader fordetermining a range rate of a vehicle-mounted backscatter transponder ina roadway. The reader includes a transmitter to generate a continuouswave signal having a carrier frequency; an antenna to transmit thecontinuous wave signal and to receive a modulated reflected responsesignal from the transponder, wherein the modulation is at a modulationfrequency, and wherein the range rate is a rate of change of a distancebetween the transponder and the antenna; a mixer to mix the modulatedreflected response signal with the carrier frequency to produce adownconverted signal; a bandpass filter to filter the downconvertedsignal to pass a bandpass filtered signal containing at least themodulation frequency; a non-linear amplitude transfer function toproduce a modulation-suppressed signal when the function is applied tothe bandpass filtered signal to remove modulation; and a frequencymeasurer to measure the frequency of the modulation-suppressed signaland to determine the range rate from the measured frequency.

In one aspect, the present application describes a method of estimatingvehicle location in a roadway using an automatic vehicle identificationsystem, the system including an antenna defining a coverage area forcommunicating with a transponder mounted to a vehicle in the roadway.The method includes receiving a set of response signals from thetransponder at points in time and determining a range rate of thetransponder relative to the antenna at each point in time; identifying aminima in the magnitude of the range rate; estimating a first positionof the transponder at a first time corresponding to the occurrence ofthe minima; estimating a velocity of the vehicle based upon one or moreof the determined range rates; and estimating a second position of thetransponder based upon the first position and the velocity.

In another aspect, the present application describes an automaticvehicle identification system for identifying the position in a roadwayof a vehicle. The system comprises an antenna for communicating with atransponder mounted to the vehicle in the roadway; a transceiver forbroadcasting a continuous wave signal over the antenna and for receivingresponse signals from the transponder; a memory storing vehicle positionlocating instructions; and a processor, which when executing the vehicleposition locating instructions, is configured to determine a range rateof the transponder relative to the antenna based upon response signalsreceived at points in time, identify a minima in the magnitude of therange rate, estimate a first position of the transponder at a first timecorresponding to the occurrence of the minima, estimate a velocity ofthe vehicle based upon one or more of the determined range rates, andestimate a second position of the transponder based upon the firstposition and the velocity.

In yet a further aspect, the present application describes anon-transitory computer-readable medium storing processor-executableinstructions which, when executed, cause a processor to carry out one ofthe methods described herein.

Other aspects and features of the present invention will be apparent tothose of ordinary skill in the art from a review of the followingdetailed description when considered in conjunction with the drawings.

Reference is first made to FIG. 1, which shows, in block diagram form,an example electronic toll collection (ETC) system 10. The ETC system 10is employed in connection with a roadway 12 having one or more lanes forvehicular traffic. The arrow indicates the direction of travel in theroadway 12. For diagrammatic purposes, a vehicle 22 is illustrated inthe roadway 12. In some instances, the roadway 12 may be an accessroadway leading towards or away from a toll highway. In other instances,the roadway 12 may be the toll highway.

Vehicle 22 is shown in FIG. 1 with a transponder 20 mounted to thewindshield. In other embodiments, the transponder 20 may be mounted inother locations.

The ETC system includes antennas 18 connected to an automatic vehicleidentification (AVI) reader 17. The reader 17 generates signals fortransmission by the antennas 18 and processes signals that are receivedby the antennas 18. The reader 17 includes a processor 35 and one ormore radio frequency (RF) modules 24 (one is shown for clarity). In manyimplementations, each antenna 18 may have a dedicated RF module 24;although in some embodiments an RF module 24 may be shared by more thanone antenna 18 through time multiplexing.

The antennas 18 are directional transmit and receive antennas which, inthe illustrated embodiment, are oriented to define a series of capturezones 26 extending across the roadway 12 in an orthogonal direction. Thearrangement of capture zones 26 define the communication zone withinwhich toll transactions are conducted using an ETC communicationsprotocol.

The ETC system 10 may operate, for example, within the industrial,scientific and medical (ISM) radio bands at 902-928 MHz. For example,the ETC system 10 may conduct communications at 915 MHz. In otherembodiments, other bands/frequencies may be used, including 2.4 GHz, 5.9GHz, etc.

In this embodiment, the ETC system 10 operates using a passivebackscatter transponder. The ETC system 10, and in particular the reader17 and antennas 18, continuously poll the capture zones 26 using timedivision multiplexing or frequency division multiplexing or codedivision multiplexing to be able to suppress or ignore signals fromoverlapping capture zones 26. The polling may include broadcasting acontinuous wave RF signal and awaiting a detected response signal fromany transponder that happens to be within the capture zone 26. Theresponse signal generally includes a modulated reflected signal from thetransponder. In some cases each of the antennas 18 may include aseparate transmit antenna and receive antenna. In some other cases, eachantenna 18 includes a single antenna used for transmission and receptionand the transmit and receive paths are coupled to the antenna 18 througha circulator or other signal splitting/coupling device.

In the ETC system 10, vehicles are detected when they enter the capturezones 26 and the vehicle-mounted transponder 20 responds to the RFsignal broadcast by one of the antennas 18. The frequency of the cyclicpolling is such that as the vehicle 22 traverses the capture zones 26,the transponder 20 receives and responds to RF signals from the reader17 a number of times. Each of these poll-response exchanges may bereferred to as a “handshake” or “reader-transponder handshake” herein.

Once the reader 17 identifies the transponder 20 as a newly-arrivedtransponder 20 it will initiate conduct of an ETC toll transaction. Thismay include programming the transponder 20 through sending a programmingsignal that the transponder 20 uses to update the transponderinformation stored in memory on the transponder 20.

The ETC system 10 further includes an enforcement system. Theenforcement system may include a vehicle imaging system, indicatedgenerally by the reference numeral 34. The vehicle imaging system 34 isconfigured to capture an image of a vehicle within the roadway 12,particularly the vehicle license plate. If the vehicle fails to completea successful toll transaction, then the license plate image is used toidentify the vehicle owner and an invoice is sent to the owner. Thevehicle imaging system 34 includes cameras 36 mounted so as to capturethe front and/or rear license plate of a vehicle in the roadway 12. Avehicle detector 40 defines a vehicle detection line 44 extendingorthogonally across the roadway 12. The vehicle detector 40 may includea gantry supporting a vehicle detection and classification (VDAC) systemto identify the physical presence of vehicle passing below the gantryand operationally classifying them as to a physical characteristic, forexample height. In some example embodiments, the vehicle detector 40 mayinclude loop detectors within the roadway for detecting a passingvehicle. Other systems for detecting the presence of a vehicle in theroadway 12 may be employed, including light curtains, laser detectionsystems, and other systems.

The imaging processor 42 and vehicle detector 40 are coupled to andinteract with a roadside controller 30. The roadside controller 30 alsocommunicates with remote ETC components or systems (not shown) forprocessing toll transactions. The roadside controller 30 receives datafrom the reader 17 regarding the transponder 20 and the presence of thevehicle 22 in the roadway 12. The roadside controller 30 initiates atoll transaction which, in some embodiments, may include communicatingwith remote systems or databases. On completing a toll transaction, theroadside controller 30 instructs the reader 17 to communicate with atransponder 20 to indicate whether the toll transaction was successful.The transponder 20 may receive a programming signal from the reader 17advising it of the success or failure of the toll transaction andcausing it to update its memory contents. For example, the transponder20 may be configured to store the time and location of its last tollpayment or an account balance.

The roadside controller 30 may receive data from the vehicle imagingsystem 34 and/or the vehicle detector 40 regarding vehicles detected atthe vehicle detection line 44. The roadside controller 30 controlsoperation of the enforcement system by coordinating the detection ofvehicles with the position of vehicles having successfully completed atoll transaction. For example, if a vehicle is detected in the roadwayat the vehicle detection line 44 in a particular laneway, the roadsidecontroller 30 evaluates whether it has communicated with a vehicle thathas completed a successful toll transaction and whose positioncorresponds to the position of the detected vehicle. If not, then theroadside controller 30 causes the imaging processor 42 to capture animage of the detected vehicle's license plate or, if already capturedupstream, then the roadside controller 30 may initiate an enforcementprocess, such as an automatic or manual license plate identificationprocess followed by billing. The license plate, once identified, may becorrelated to the same license place identified at another entry/exitpoint in order to calculate the appropriate toll amount for billing.

The vehicle detection line 44 may lie outside the capture zones 26. TheETC system 100 needs to determine the likely position or path of atransponder with which it has communicated to determine when and wherethat transponder would likely have crossed the vehicle detection line44. Then it can correlate transponders with vehicle images.

There are some existing solutions for determining vehicle location in anETC system. One is to provide multiple sets of roadside readers toconduct narrow beam sweeping as vehicle approach the capture zones.Using readers on either side of the roadway, the intersecting beams towhich a transponder responds give an indication of likely position. Thissolution requires the installation of additional roadside equipment andmay not be suitable for all installations, particularly passivebackscatter systems, since it requires a long lead time into the zone,narrow quick moving beams, and may rely upon RSSI measurements.

Another solution is to use additional roadside receivers to receive thetransponder transmissions in conjunction with monopulse antennas. Theseantennas permit direction of arrival to be determined and with two ofthese the location of the vehicle can be determined. This solutionrequires the installation of additional roadside equipment and may notbe suitable for all installations. It may be better suited to an activetransponder system since in a passive transponder system the readertransmission picked up by the receivers will swamp out the transpondersignals and degrade the monopulse operation. There are also solutionsaimed at determining the lane in which a vehicle is likely travelling.So-called “voting” algorithms make a lane assignment decision based uponthe number of handshakes completed with each antenna, sometimes using aweighting algorithm or other techniques. These solutions, however, onlyindicate the likely lateral position of a vehicle in the roadway at thetime the vehicle is traversing the capture zones 26.

In accordance with one aspect of the present application, the ETC system10 determines the Doppler shift associated with signals received by theantennas 18 from the transponder 20. The Doppler shift correlates to arange rate, i.e. the rate at which the distance between the transponder20 and the antenna 18 is changing; in other words, the transponder speedtowards or away from the antenna (note that the antennas 18 aretypically elevated above the roadway and the vehicle moves tangential tothe antenna 18). The range rate reaches a zero-crossing point when thetransponder passes under the gantry holding the antenna such that it isthen moving away from the antenna rather than towards the antenna.Accordingly, if the ETC system 10 determines the zero-crossing point ofa transponder's range rate, it then knows the point at which it crossesunder the gantry. Using one or more previous (or later) range ratemeasurements from previous (or later) transponder signals, the velocityof the vehicle may then be estimated at prior (or later) points in time,thereby allowing for estimation of a likely path of the vehicle towards(or away from) the antenna. In some of the following examples, thevehicle detection point is presumed to be upstream from the capturezones; thus, the ETC system 10 seeks to estimate the vehicle position atan earlier point in time based upon range rate measurements fromtransponder signals. Nonetheless, it will be appreciated that similartechniques may be used to determine position downstream at a later pointin time using later range rate measurements.

In one example, the zero-crossing point and a single earlier range ratemeasurement is used to determine a range of velocity estimates (based ona bounded range of transponder heights, and a bounded range of angles oftravel towards the antenna and lateral offsets from the antenna), which,assuming constant velocity, correlate to a range of estimate vehiclepositions at previous points in time. This range of path and speedestimates is then used to estimate likely vehicle position at time ofcrossing the vehicle detection line. The estimate of vehicle position atthe time of crossing the vehicle detection line may then be correlatedto physically detected vehicle data.

In another example, multiple range rate measurements are determined andcorresponding velocity estimates determined for those points in time.Using curve-fitting, the vehicle's velocity and position at variouspoints in time may then be estimated, with the range estimates beingconstrained by bounds on transponder height, angles of travel, andlateral offsets of the vehicle path from the antenna. In some cases, twosets of estimates may be determined corresponding to signals received bytwo of the antennas. The two sets of estimates may then be compared tofind points of intersection among the ranges of estimatedpaths/velocities to arrive at a more accurate subset of estimates andmay also be used to determine the angle of travel across the road.

In yet another example, the range-rate-based position estimation processis combined with other position locating systems, such as a laneassignment system, to improve accuracy of the position estimate.

Range Rate Determination

The first difficulty that arises in implementing embodiments of theposition locating system is determining the range rate for atransponder. In an ETC system, the antenna is stationary and the RFIDdevice (transponder) is in motion; however similar issues would arise inthe case of a moving reader/antenna and a stationary RFID device, or inthe case of both the reader and RFID device moving.

In a backscatter-based system, the reader broadcasts an RF signaltowards the RFID device and receives back a reflected signal. The RFIDdevice imposes modulation onto the reflected signal, which is detectedand demodulated by the reader.

In the case of vehicular systems of the type discussed herein,particularly at highway speeds, the Doppler shift is not constant withtime and manifests as a large time-varying phase shift over the durationof a single modulation packet from the RFID device. This makes recoveryof the modulation and detection of the Doppler shift challenging.Measuring Doppler shift in conventional radar or such systems typicallyinvolves directly measuring the phase shift of a reflected signalrelative to a transmitted signal. By measuring that phase shift overtime, the Doppler shift can be used to determine the speed of the RFIDdevice and/or changes in speed.

In the case of vehicle-mounted RFID, the phase of the received signalincludes the reflected signal from the RFID device, but also distortioncomponents that introduce errors in the phase measurements. Distortioncan arise from transmit leakage into the receiver, reflections fromother items, non-idealities in the receiver signal/circuit path like DCoffsets, multi-path reflections of stationary and moving objects, andreflection of the signal from vehicles, including the vehicle with theRFID device.

A high signal-to-noise ratio (SNR) is typically required to directlymeasure phase with sufficient accuracy to determine Doppler shift. Withbackscatter RFID, because of the modulation imposed on the reflectedsignal and the variability of modulation rate between RFID devices,there is little SNR available for direct measurements of phase shift ofthe received reflected signal.

In accordance with one aspect of the present application, Doppler shiftand/or range rate may be determined by exploiting the fact thatbackscatter modulation in RFID devices manifests itself as bipolaramplitude modulation of the received signal. At the reader, thereflected signal is downconverted to baseband and bandpass filtered topass the modulated portion of the Doppler-shifted reflected signal. Thatfiltered signal is then adjusted through application of a non-linearamplitude transfer function that serves to effectively remove themodulation and leave a modified signal from which the Doppler shift canbe directly measured.

Reference is now made to FIG. 2, which shows a simplified block diagramof an RFID reader 100 for determining Doppler shift in a backscatterRFID system. The RFID reader 100 includes a transmitter 102 and atransmit antenna 104. The RFID reader 100 further includes a receiveantenna 106, although in some embodiments the transmit antenna 104 andthe receive antenna 106 are the same antenna, which is then coupled tothe transmitter 102 and receiver circuitry through a circulator or othersignal splitting/combining device.

The transmitter 102 generates and broadcasts an RF signal using thetransmit antenna 104. The transmitted RF signal may be defined as:

A_(T)·cos(w_(T)·t)

In this expression, A_(T) is the transmit signal magnitude, w_(T) is thefrequency in radians, and t is the instantaneous time.

An RFID device (not shown) receives the RF signal and returns areflected signal. The RFID device imposes modulation on the reflectedsignal. The reflected signal is received by the RFID reader 100 via thereceive antenna 102. The reflected signal from any object in the fieldmay be expressed as:

${A_{T} \cdot \left( {L_{x}(t)} \right)^{2} \cdot {O_{x}(t)} \cdot \left( {\cos \left( {w_{T}\left( {t - {2\frac{d_{x}(t)}{c}}} \right)} \right)} \right)} = {{R_{x}(t)} \cdot {\cos \left( {\left( {w_{T} + {w_{x}(t)}} \right) \cdot t} \right)}}$

The index x denotes the object from which the signal is reflected, whichmay include stationary or moving objects, including vehicles. In theabove expression, L_(x)(t) is the RF power loss for a signal betweentransmission and receipt of the reflection. It includes the gain of thesubsystem antennas in the direction of the object as well as propagationeffects. If the object is moving it will be time dependent. It isunipolar (i.e. it can only have positive or negative values) within theregion of interest. O_(x)(t) is the amount of reflection by the objectin the direction of the receive antenna. It is time dependent if theobject is moving. It is also unipolar in the region of interest.

The term d_(x)(t) denotes the distance (range) between the object andthe receive antenna. It is time dependent if the object is in motion.The speed of RF propagation is given by c. The term R_(x)(t) is themagnitude of the received signal, and it includesA_(T)·(L_(x)(t))²·O_(x)(t). The Doppler shift in radians is given byw_(x)(t) if the object is moving. Expressed in Hz, the Doppler shift isf_(x)(t). Note that:

${f_{x}(t)} = {{- 2} \cdot \frac{f_{T}}{c} \cdot \frac{\left( {d_{x}(t)} \right)}{t}}$

In this expression, f_(T) is the frequency of the transmit signal andd(d_(x)(t))/dt is the differential of the range with respect to time,i.e. the range rate or velocity of the object relative to the receiveantenna.

The reflected signal from the RFID device itself may be expressed as:

${{m_{r}(t)} \cdot A_{T} \cdot \left( {L_{r}(t)} \right)^{2} \cdot {O_{r}(t)} \cdot \left( {\cos \left( {w_{T}\left( {t - {2\frac{d_{r}(t)}{c}}} \right)} \right)} \right)} = {{m_{r}(t)} \cdot {R_{r}(t)} \cdot {\cos \left( {\left( {w_{T} + {w_{r}(t)}} \right) \cdot t} \right)}}$

In the above expression, the term m_(r)(t) denotes the modulationimposed by the RFID device on the reflected signal. The index rindicates that the terms relate to the RFID device, as opposed to otherobjects in the field. Note that the item of particular interest isw_(r)(t), which is the Doppler shift radian frequency for the signalfrom the moving RFID device. In Hz, this may be expressed as:

${f_{r}(t)} = {{- 2} \cdot \frac{f_{T}}{c} \cdot \frac{\left( {d_{r}(t)} \right)}{t}}$

Referring still to FIG. 2, the received reflected signal at the receiveantenna 106 is downconverted using a carrier frequency signal (plus someconstant phase shift θ) from the transmitter 104 and a combiner 108. Thedownconverted signal may be expressed as:

m_(r)(t)·R_(r)(t)·cos((w_(T)+w_(r)(t))·t)·cos(w_(T)·t+θ)

This may also be expressed as:

=0.5·m _(r)(t)·R _(r)(t)·cos(2w _(T) ·t+w _(r)(t)·t+θ)+0.5·m _(r)(t)·R_(r)(t)·cos(w _(r)(t)·t−θ)

The first term is at twice the carrier frequency and the second term isat baseband with respect to the carrier. It will be noted that thesecond term includes the time-dependent modulation m_(r)(t) and thetime-dependent changes in reflectivity and power loss resulting frommovement of the RFID device. It will also be appreciated that themixing/downconversion will produce other products, generally at highermultiples of the carrier frequency. For the purposes of the presentanalysis, these terms are ignored since they will be filtered from thedownconverted signal.

Note that the received signal will include other reflected signals inaddition to the modulated reflected signal from the RFID device. Afterdownconversion, these other signals will be given by:

0.5·R _(x)(t)·(cos(2w _(T) ·t+w _(x)(t)·t+θ)+cos(w _(x)(t)·t−θ))=0.5·R_(x)(t)·(cos(2w _(T) ·t+w _(x)(t)·t+θ))+0.5·R _(x)(t)·cos(w _(x)(t)·t−θ)

As noted above, the modulation m_(r)(t) from an RFID device may berepresented as a bipolar phase modulation or a bipolar amplitudemodulation, with some mean offset. In the case of bipolar amplitudemodulation, the modulation is expressed as:

m _(r)(t)=a ₁ +a _(m) ·H _(r)(t)

In this expression, a₁ is the mean offset, a_(m) is the magnitude of thesignal change, and H_(r)(t) is one of two states: (1, −1). As a specificcase, in on-off keying a₁≧a_(m).

Bipolar phase modulation may be expressed as:

m _(r)(t)=a ₁ +a ₂·cos(G _(r)(t)+φ)

In the above expression, Gr(t) can take one of two states: (0, π). Thisexpression is then equivalent with:

m _(r)(t)=a ₁ +a ₂·cos(G _(r)(t))·cos(φ)=a ₁ +a _(m) ·H _(r)(t)

In other words, the bipolar phase modulation (so defined) may be treatedthe same as bipolar amplitude modulation.

If the above expression for bipolar modulation is substituted into theexpression for the downconverted modulated reflected signal, then itbecomes:

0.5·(a ₁ +a _(m) ·H _(r)(t))·R _(r)(t)·(cos(2w _(T) ·t+w_(r)(t)·t+θ)+cos(w _(r)(t)·t−θ))=0.5·(a ₁ +a _(m) ·H _(r)(t))·R_(r)(t)·(cos(2w _(T) ·t+w _(r)(t)·t+θ))+0.5·a ₁ ·R _(r)(t)·cos(w_(r)(t)·t−θ)+0.5·a _(m) ·H _(r)(t)·R _(r)(t)·cos(w _(r)(t)·t−θ)

The following observation may be made regarding the frequency componentsof some of the time-dependent terms in the above expressions. For anyreasonable Doppler rate, it will be appreciated that:

$\frac{\left( {H_{r}(t)} \right)}{t}\operatorname{>>}{\frac{\left( {f_{x}(t)} \right)}{t} > \frac{\left( {R_{x}(t)} \right)}{t} \approx \frac{\left( {R_{r}(t)} \right)}{t}}$

In other words, the rate of change of the signal magnitude due tochanges in propagation loss and reflectivity due to movement of theobject or RFID device will be less than the rate of change in theDoppler shift, which in turn is much less than the modulation rate.

Accordingly, referring again to FIG. 2, a bandpass filter 110 may beused to filter the downconverted signals and pass the modulationfrequencies, rejecting any terms that contain multiples of the carrierfrequency (too high) or any terms that are not modulated (too low). Withsuch a bandpass filter 110, we eliminate both terms of the signalreflected from other objects, and eliminate two terms of the modulatedreflected signal from the RFID device, and are left with:

0.5·a_(m)·H_(r)(t)·R_(r)(t)·cos(w_(r)(t)·t−θ)

This band-pass filtered signal may further be expressed as:

K_(m)(t)·cos(w_(r)(t)·t−θ)

The term K_(m)(t) is a time-dependent amplitude function that containsboth the effects of signal attenuation and the RFID-imposed modulationH_(r)(t), thereby meaning it is bipolar. The signal further includes theperiodic amplitude function cos(w_(r)(t)·t−θ), which is also bipolar andis solely dependent upon the Doppler frequency.

The modulation may then be removed from the bandpass-filtereddownconverted reflected signal by applying a non-linear amplitudetransfer function 112. Examples of the non-linear amplitude transferfunction 112 include a square law function or an absolute magnitudefunction. The non-linear amplitude transfer function 112 addresses thefact that both phase contributors have bipolar magnitudes. Byeliminating the bipolar behaviour of the K_(m)(t) term, the modulationis effectively removed as a phase contributor from the signal for thepurpose of analyzing the Doppler effect.

An example is now described with respect to the square law function. Theunipolar output after squaring the bandpass-filtered downconvertedsignal is:

$\begin{matrix}{{\left( {K_{m}(t)} \right)^{2} \cdot {\cos^{2}\left( {{{w_{r}(t)} \cdot t} - \theta} \right)}} = {\left( {K_{m}(t)} \right)^{2} \cdot \left( {1 + {\cos \left( {{2{{w_{r}(t)} \cdot t}} - {2\theta}} \right)}} \right)}} \\{= {\left( {K_{m}(t)} \right)^{2} + {\left( {K_{m}(t)} \right)^{2} \cdot {\cos \left( {{2{{w_{r}(t)} \cdot t}} - {2\theta}} \right)}}}}\end{matrix}$

From the definition above of K_(m)(t), the following observations may bemade:

(K_(m)(t))² ∝ (L_(r)(t))⁴·(O_(r)(t))²·(H_(r)(t))²

But from the definition of H_(r)(t), the square of it will be equalto 1. Accordingly:

(K_(m)(t))² ∝ (L_(r)(t))⁴·(O_(r)(t))²

A filter 114 is then applied to the resulting squared signal. The filter114 may include a low-pass filter that suppresses any residualmodulation frequencies or noise content. A bandpass filter may also beused to suppress the stand alone term (K_(m)(t))². Because the highestfrequency that the filter 114 is required to pass is the Dopplerfrequency, the filter bandwidth will be very much less than any filterrequired for demodulation and hence a high SNR can be obtained even whenthe SNR in the modulation bandwidth is poor. The effect of the filterwill be to average the amplitude function (K_(m)(t))² so what is outputfrom the filter 114 is the signal:

K_(a)(t)·cos(2w_(r)(t)·t−2θ)

In this expression, K_(a)(t) is a relatively slowly-varying averageamplitude function dependent upon (L_(r)(t))⁴·(O_(r)(t))². It istherefore unipolar and non-zero. The term cos(2w_(r)(t)·t−2θ) is aperiodic amplitude function at twice the Doppler frequency, and isbipolar. As a result, the Doppler frequency may then be determined in afrequency measurement 116 stage by, for example, detecting zerocrossings of the filtered squared signal.

In another example, the non-linear amplitude transfer function 112 isimplemented using an absolute magnitude function. In this example, inone implementation the polarity is discarded from the signal output fromthe bandpass filter 110. The result of such an operation is:

|K _(m)(t)|·|cos(w _(r)(t)·t−θ)|=|(L _(r)(t))² ·O _(r)(t)|·|H_(r)(t)|·|cos(w _(r)(t)·t−θ)|

As in the case of the square law, the magnitude of the modulationfunction H_(r)(t) is equal to 1, so it may be eliminated from theanalysis.

Applying the filter 114 to suppress residual modulation frequency ornoise content improves the SNR. The effect of such filtering is toaverage the amplitude function |K_(m)(t)| such that the filteredmagnitude signal is given by:

K_(b)(t)·|cos(w_(r)(t)·t−θ)|

The term K_(b)(t) is a slowly-varying average amplitude functiondependent upon |(L_(r)(t))²·O_(r)(t)|, and it is therefore unipolar andnon-zero if an RFID signal is present. It will be appreciated that theDoppler component, |cos(w_(r)(t)·t−θ)|, exhibits two amplitude minimaevery period of f_(r)(t). By, for example, measuring the time betweenthe minima the Doppler frequency is directly obtained.

It may also be observed that the term |cos(w_(r)(t)·t−θ)| gives the sameanswer for negative or positive Doppler shifts. This ambiguity may beresolved through multiple observations of the Doppler frequency toassess whether it is increasing or decreasing, which correspond to theRFID device moving away or moving towards the receive antenna 106,respectively.

In some embodiments, the modulation function H_(r)(t) is not restrictedto the set (−1, 1). For example, the function may have time-shaped bits.Nevertheless, the above-described processes may still be applied,provided the average amplitude of positive and negative states are equaland as long as the modulation rate remains much higher than the Dopplerrate to allow for the filtering process.

In some embodiments, the transmit signal may be phase (or bipolaramplitude) modulated and the process will still lead to the Dopplerfrequency provided that the modulation is passed through thedown-conversion filter and then removed (averaged out) by thepost-down-conversion non-linear amplitude transfer function.

It will be appreciated that the above-described method requires only asingle receive path, i.e. it does not require the phase of the incomingsignal to be determined and it removes the modulation to determine theDoppler shift directly.

The above-described process may be modified, in some embodiments, usingquadrature down-conversion. For example, both the in-phase andquadrature paths may be independently processed (band-pass filtered,modified by non-linear transfer function, and filtered), using e.g. themagnitude function approach, to result in signals such as:

I=K _(b)(t)·|cos(w _(r)(t)·t)|

Q=K _(b)(t)·|sin(w _(r)(t)·t)|=K _(b)(t)·|cos(π/2−w _(r)(t)·t)|

The in-phase component will have minima at w_(r)(t)·t=0+n·π, and thequadrature component will have minima at w_(r)(t)·t=π/2+n·π. Bycomparing the time difference between the minima on the two channels, aknown fraction of Doppler period is determined and, hence, the Dopplerfrequency.

The Doppler frequency measurement is not restricted to using minima.Since frequency is the rate of change of phase with time, by determiningthe phase change over any part of a transmission and knowing the time,the frequency can be measured.

Location Determination

As described above, the ETC system may determine the range rate (speedof the RFID device relative to the reader antenna) using RFID modulatedreflected signals for each of the signals. This data may be used todetermine, i.e. estimate, the vehicular speed and likely position of thevehicle and RFID device at the times during which the reflected signalswere sent and, based on that data, the likely position of the vehicle atother points in time.

The easiest case is one in which the vehicle is constrained to travel ina known longitudinal path without wide lateral variation in position.This may occur in the case of a set of rail tracks or in the case of asingle lane highway or roadway.

Reference is now made to FIG. 3, which illustrates a side view of anexample ETC system 200, in which vehicles are constrained to travel in asingle lane. The constraint is such that the system is modeled in2-dimensions with a vehicle 202 travelling a fixed vector passing belowan elevated antenna 204. The vehicle 202 is equipped with a transponder206 mounted to its windshield. In other embodiments, the transponder 206may be mounted elsewhere on the vehicle 202. In general, transpondersare usually located between about 3 to 8 feet above the surface of theroadway.

The antenna 204 is a directional antenna that defines a coverage area208 (i.e. capture zone) within which it is generally able to communicatewith and receive response signals from transponders 206.

It will be appreciated that as the vehicle 202 travels through thecoverage area 208 at vehicular roadway speed, the transponder 206receives transmit signals from the antenna 204 and responds bymodulating a reflected signal. As described above, the reader (notillustrated) may determine a range rate for the transponder 206 basedupon the modulated reflected signal received at the antenna 204. Basedon one or more range rate measurements, the roadway velocity of thevehicle 202 may be estimated. With an estimated position at one point intime and an estimated velocity vector, the position of the transponder206, and thus the vehicle 202, may then be estimated at other points intime.

Accordingly, the system 100 determines (i.e. estimates) the position ofthe transponder 206 at one point in time. One point that may be used insome embodiments is the point at which the transponder 206 passesdirectly under the antenna 204. At this point, the range rate crosseszero. In other embodiments, different positions may be used. For examplea vehicle detection sensor, such as a loop detector, light curtain orscanner may be used to pinpoint the location of the vehicle at a givenpoint in time. Note that the latter techniques would still need to becorrelated with transponder communications to associate range ratemeasurements to the vehicle position, whereas the range ratezero-crossing approach is already correlated to a particular transponder206.

The range rate at any point in time a function of four variables: thevehicle velocity (v); the height (h) between the antenna and thetransponder; the distance (d(t)) of the transponder along the vehicletrajectory; and the communication carrier frequency (f_(T)) of thebackscatter RFID system.

Assume that at time t=0, d(t)=0. Then the following expressionsgenerally apply:

d(t) = t ⋅ v${r\left( {t\; 1} \right)} = \sqrt{{d\left( {t\; 1} \right)}^{2} + h^{2}}$${f_{d}\left( {t\; 1} \right)} = {{- 2} \cdot \frac{f_{T}}{c} \cdot \frac{\left( {r\left( {t\; 1} \right)} \right)}{t}}$

In the above expression, r(t1) is the range at time t1, f_(d)(t1) is theDoppler measurement at time t1, and c is the speed of RF propagation.Accordingly, it will be appreciated that, with the Doppler measurementat time t1 calculated from the transponder response signal, the system100 may then determine the rate of change of r(t1), i.e. the range rate.

The size z of the coverage area 208 is generally known. It is not afixed value since, depending on the age of the transponder 206, itsmounting configuration, environmental factors, etc., differenttransponders 206 may be able to communicate with the antenna 206 overslightly different sized zones. Nonetheless, a bounded range z ofreasonable position values is known for a given installation. Forexample, a coverage area 208 that is nominally 12 feet long maypractically be considered as being between about 8 and 15 feet long.

The length of time that the transponder 206 is in communication with theantenna 204 is also known. Thus the time it takes the vehicle 202 totraverse the coverage area 208 is known. Therefore, based on the rangeof size z values, there is a range of possible v values for the vehicle202. This gives a reasonable set of bounded estimates for velocity v,which then are iteratively tested for fit with the Dopplermeasurement(s).

As an example, suppose that at time t1, a range rate of 12.89 m/s iscalculated from the Doppler measurement. The antenna 204 is mounted 17ft above the roadway and the transponder height is assumed to be 4 ft.The coverage area 208 size z is between 8 and 15 feet. The transponder206 is in communication for 115.5 ms. The range rate zero-crossing pointoccurs at a time of t0=t1+80.85 ms. Based on a bounded range ofvelocities v between 80 and 150 kph, the velocities may be tested todetermined which velocity results in a range rate of 12.89 m/s at timet1. The resulting estimated velocity v in this example situation is 96.5kph.

Accordingly, with this estimated velocity, and estimated positions ofthe vehicle 202 at times t0 and t1, the vehicle position at other times,such as t2 or t3, may then be estimated.

It has been determined empirically that the transponder height has anearly negligible impact on position estimates since the antenna heighttends to be much larger than the transponder height. Nonetheless, thetransponder height may be treated as a bounded range, thereby resultingin a range of estimated velocity values.

With more than one range rate measurement, more than one estimate forvelocity may be obtained. The velocities thus obtained may be averaged,or a curve may be fit to the velocity estimates to account for possiblevelocity changes as the vehicle traverses the coverage area 208.

A more complex problem is determining the position of a vehicle in amulti-lane environment in which it cannot be assumed that the vehicletravels in a constrained path. Reference is now made to FIG. 4, whichshows an overhead view of one example of an ETC system 250. Threevehicles 202, denoted 202 a, 202 b, and 202 c, are shown. Each vehicle202 is shown in a first position (Pos1) and a second position (Pos2).One antenna 204 is shown in this example.

The first vehicle 202 a is shown travelling parallel to the edge of theroadway with no lateral offset from the antenna 204, as in theconstrained travel example illustrated previously. The second vehicle202 b is shown travelling parallel to the edge of the roadway offsetfrom the antenna 204. The distance of the offset is a cross-trackdistance x. The relationship between the range r, height h, distance d,and cross-track distance x may now be expressed as:

r(t1)=√{square root over (d(t1)² +h ² +x ²)}

Note that there is still a minima in range rate that occurs where thevehicle direction of motion/path is orthogonal to the antenna.

The third vehicle 202 c is shown travelling at an angle θ from parallelto the centerline of the roadway and offset from the antenna 204 by thecross-track distance x.

It has been experimentally noted that, like antenna height h, thecross-track distance for reasonable ranges of x has a near negligibleimpact on the correlation between range-rate measurements andvelocity/distance estimates. Nonetheless, a bounded range of cross-tracedistances x may be assumed, resulting in a bounded range ofvelocity/distance estimates for a given range-rate measurement.

Recall that in a multi-lane system, there are multiple antennas thatspan the roadway, and that the system selects the antenna with the best(e.g. highest number of) communications with the vehicle-mountedtransponder. That antenna will usually tend to be the antenna to whichthe vehicle passes most closely, although such is not necessarily thecase depending on environmental factors, antenna age and anomalies, andmultipath reflections. Therefore, there is an upper bound of reasonablex values on either side of an antenna, above which it may be presumedthat the vehicle would better communicate with another antenna.Similarly, in a multi-lane open road environment, there is an upperbound on the angle θ at which a vehicle is able to travel relative tothe roadway centerline without veering off the roadway. In oneembodiment, the bounds on the angle θ may be related to the time in thecapture zone, since the faster that the vehicle is travelling, the lesslikely that it is travelling at a large angle θ relative to thecenterline.

Accordingly, given a range rate minima at one time t0 and a range ratemeasurement at one or more other times, t1, we may estimate a boundedregion in which the vehicle is likely located at a third time.

Reference is now made to FIG. 5, which diagrammatically shows anoverhead view of a vehicle location system 300. The system 300 includesone antenna 302. A range rate minima is detected at time t0, whichcorresponds to a location under the antenna 302 or along a cross-trackoffset x from the antenna orthogonal to the direction of travel. At atime t1, a range rate is calculated based on a Doppler measurement. Thebounded set of possible locations is indicated by numeral 304 based on abounded set of velocities and corresponding possible cross-track offsetsx and angles θ corresponding to those velocities. Each location withinthe bounded set of locations 304 corresponds to a unique combination ofvelocity v, cross-track offset x and angle θ. Each then (presumingconstant velocity and direction of travel) corresponds to a predictedlocation at time tn. Thus, the system 300 is able to predict thepossible locations of the vehicle at a time tn. In this example, at thetime tn, the range of possible locations is indicated by referencenumeral 306.

In another embodiment, the system 300 evaluates whether it is possiblefor the vehicle to be in a particular location at a time tn based uponwhether that location falls within the bounded set of possiblelocations. This embodiment may be used to determine whether a physicallydetected vehicle may be correlated to a transponder-equipped vehiclewith which the system 300 has communicated. In yet another embodiment,the system 300 predicts a range of possible times at which the vehiclewill reach a vehicle detection line, based on the range of possiblevelocities v and trajectories (x and θ).

Reference is now made to FIG. 6, which diagrammatically shows anoverhead view of a vehicle location system 400 in a multi-laneenvironment that includes a plurality of antenna 402 a, 402 b, 402 c,402 d, and 402 e. In this embodiment, multiple range rate measurementsare calculated, corresponding to times t1, t2 and t3. The range ofvelocities and corresponding positions based upon the first range ratemeasurement at time t1 is indicated using reference numeral 406. Therange of velocities and corresponding positions based upon the secondrange rate measurement at time t2 is indicated using reference numeral408. The plurality of range rate measurements assists in narrowing therange of possible velocities that meet the criteria (for velocity,angle, and offset) in both sets of data and, thus, the range of possiblelocations at the time tn. As a result a narrower range of possiblelocations 410 at time tn is determined.

In some embodiments, the range rate measurements may be averaged orotherwise combined. In some cases, the calculated bounded set ofvelocities (and their x and θ values) for one range rate measurement iscombined with the corresponding bounded set of velocities (and theircorresponding x and θ values) of other range rate measurements to arriveat a subset of possible velocities and their corresponding x and θvalues. The combination may take into account possible reasonableacceleration or deceleration between two points in time.

Reference is now made to FIG. 7, which shows a graph 500 of range ratecalculated versus time. It will be understood that the range ratecalculations correspond to (nearly) discrete points in time at which aresponse signal is received by the system from a transponder. In thisexample, five range rate calculations are shown at times t1, t2, t3, t4,and t5. Also in this example, it is presumed that the sign of the phaseshift is not known from the above measurement analysis, leaving thesystem 300 with only range rate magnitude at the specific points intime. It will be understood that the measurement times do notnecessarily include a measurement at exactly time t0 during which therange rate is zero.

One approach, illustrated in FIG. 7, is to fit a curve to the measuredrange rate magnitudes and, having found a best fit curve, to identifythe time at which that curve is at a minima. This is then identified astime t0. The curve fitting may be based upon fitting a second-degreepolynomial, in this example. Least squares may be the basis for findinga best fit, in some implementations.

Another approach, illustrated by a graph 502 shown in FIG. 8, is toiteratively change, starting at the last measurement, the measured rangerate magnitude negative and attempt to fit a curve to the data points.This iteration is performed until the best fit is realized. Thezero-crossing point and slope may then be determined from the curve. Itwill be noted that the curve may be a first-degree polynomial in someimplementations. In some implementations, the system 300 may attempt tofit a third-degree polynomial to the data points instead of afirst-degree polynomial. With the third-degree polynomial the inflectionpoint may correspond to the zero-crossing point. Least squares may beused to identify the best fit.

Referring now to FIG. 9, which shows another overhead view of a vehiclelocation system 600, it will be noted that the range of possiblelocations may be further constrained in the case where the vehicle maybe presumed to be on one side of an antenna 602, thus reducing the rangeof cross-track offsets x to one side of the antenna 602. Thisdetermination may be based, for example, upon communications received byan adjacent antenna 604 as compared to communications received by anadjacent antenna 606 on the other side of the antenna 602. Thedetermination may be based on relative handshake counts, RSSImeasurements, or other such data.

As illustrated in FIG. 9, the range rate measurements taken by bothantennas may be used to constrain the possible locations, trajectoriesand velocities, leading to a more accurate estimate of vehicle locationat time tn.

Referring again to FIGS. 1 and 2, the reader 17, RF module 24, roadsidecontroller 30, system 100, or parts thereof, may be implemented by wayof programmable integrated circuit components, application-specificintegrated circuits, analog devices, or combinations of thosecomponents. In some cases, the functions or operations described hereinmay be implemented by way of processor-executable instructions stored ona processor-readable memory that, when executed, cause one or moreprocessors to carry out those functions or operations. Some of the abovedescribed functions may be implemented by the reader 17 and some by theroadside controller 30, depending on the implementation chosen.

The present invention may be embodied in other specific forms withoutdeparting from the spirit or essential characteristics thereof. Certainadaptations and modifications of the invention will be obvious to thoseskilled in the art. Therefore, the above discussed embodiments areconsidered to be illustrative and not restrictive, the scope of theinvention being indicated by the appended claims rather than theforegoing description, and all changes which come within the meaning andrange of equivalency of the claims are therefore intended to be embracedtherein.

What is claimed is:
 1. A method of determining a range rate of avehicle-mounted backscatter transponder in a roadway using an automaticvehicle identification system, the system including an antenna defininga coverage area for communicating with the backscatter transponder, therange rate being a rate of change of a distance between the transponderand the antenna, the method comprising: transmitting, via the antenna, acontinuous wave signal having a carrier frequency; receiving a modulatedreflected response signal from the transponder, wherein the modulationis at a modulation frequency; converting the modulated reflectedresponse signal to a downconverted signal by mixing the modulatedreflected response signal with the carrier frequency; bandpass filteringthe downconverted signal to pass a bandpass filtered signal containingat least the modulation frequency; applying a non-linear amplitudetransfer function to the bandpass filtered signal to remove modulationand produce a modulation-suppressed signal; measuring the frequency ofthe modulation-suppressed signal; and determining the range rate basedupon a Doppler shift corresponding to the measured frequency of themodulation-suppressed signal.
 2. The method claimed in claim 1, whereinthe modulation comprises either bipolar phase modulation or bipolaramplitude modulation.
 3. The method claimed in claim 2, wherein themodulation comprises on-off keying.
 4. The method claimed in claim 1,wherein the bandpass filter has a low cut-off that passes the modulationfrequency and attenuates the downconverted carrier frequency, and a highcut-off that is below the carrier frequency.
 5. The method claimed inclaim 1, wherein the non-linear amplitude transfer function comprises asquare function, and applying the non-linear amplitude transfer functioncomprises squaring the bandpass filtered signal.
 6. The method claimedin claim 1, wherein the non-linear amplitude transfer function comprisesan absolute magnitude function, and applying the non-linear amplitudetransfer function comprises discarding the polarity of the bandpassfiltered signal.
 7. The method claimed in claim 1, wherein measuring thefrequency includes detecting zero-crossings of the modulation-suppressedsignal.
 8. The method claimed in claim 1, wherein measuring thefrequency includes detecting amplitude minima of themodulation-suppressed signal.
 9. A reader for determining a range rateof a vehicle-mounted backscatter transponder in a roadway, the readercomprising: a transmitter to generate a continuous wave signal having acarrier frequency; an antenna to transmit the continuous wave signal andto receive a modulated reflected response signal from the transponder,wherein the modulation is at a modulation frequency, and wherein therange rate is a rate of change of a distance between the transponder andthe antenna; a mixer to mix the modulated reflected response signal withthe carrier frequency to produce a downconverted signal; a bandpassfilter to filter the downconverted signal to pass a bandpass filteredsignal containing at least the modulation frequency; a non-linearamplitude transfer function to produce a modulation-suppressed signalwhen the function is applied to the bandpass filtered signal to removemodulation; and a frequency measurer to measure the frequency of themodulation-suppressed signal and to determine the range rate from themeasured frequency.
 10. The reader claimed in claim 9, wherein themodulation comprises either bipolar phase modulation or bipolaramplitude modulation.
 11. The reader claimed in claim 10, wherein themodulation comprises on-off keying.
 12. The reader claimed in claim 9,wherein the bandpass filter has a low cut-off that passes the modulationfrequency and attenuates the downconverted carrier frequency, and a highcut-off that is below the carrier frequency.
 13. The reader claimed inclaim 9, wherein the non-linear amplitude transfer function comprises asquare function to square the bandpass filtered signal.
 14. The readerclaimed in claim 9, wherein the non-linear amplitude transfer functioncomprises an absolute magnitude function that discards the polarity ofthe bandpass filtered signal.
 15. The reader claimed in claim 9, whereinthe frequency measurer is configured to detect zero-crossings of themodulation-suppressed signal.
 16. The reader claimed in claim 9, whereinthe frequency measurer is configured to detect amplitude minima of themodulation-suppressed signal.
 17. A non-transitory computer-readablemedium storing processor-executable instructions which, when executed,cause a processor to carry out the method claimed in claim 1.